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$$$\frac{t}{50}$$$の導関数
入力内容
$$$\frac{d}{dt} \left(\frac{t}{50}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ を $$$c = \frac{1}{50}$$$ と $$$f{\left(t \right)} = t$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dt} \left(\frac{t}{50}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dt} \left(t\right)}{50}\right)}$$$$$n = 1$$$ を用いて冪法則 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ を適用すると、すなわち $$$\frac{d}{dt} \left(t\right) = 1$$$:
$$\frac{{\color{red}\left(\frac{d}{dt} \left(t\right)\right)}}{50} = \frac{{\color{red}\left(1\right)}}{50}$$したがって、$$$\frac{d}{dt} \left(\frac{t}{50}\right) = \frac{1}{50}$$$。
解答
$$$\frac{d}{dt} \left(\frac{t}{50}\right) = \frac{1}{50}$$$A
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